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Holt Algebra 1
8-3 Factoring x2 + bx + c
Warm Up
1. Which pair of factors of 8 has a sum of 9?
2. Which pair of factors of 30 has a sum of –17?
Multiply.
1 and 8
r2 – 4r – 45
–2 and –15
x2 + 5x + 63. (x +2)(x +3)
4. (r + 5)(r – 9)
Holt Algebra 1
8-3 Factoring x2 + bx + c
Simplify.
c.
5
41 4 4m
mn
n
Holt Algebra 1
8-3 Factoring x2 + bx + c
Factor quadratic trinomials of the form x2 + bx + c.
Objective
Holt Algebra 1
8-3 Factoring x2 + bx + c
Factor each trinomial by guess and check.x2 + 10x + 24
4 6x x
ProductSum
Holt Algebra 1
8-3 Factoring x2 + bx + c
3 4x x
ProductSum
Factor each trinomial by guess and check.x2 + 7x + 12
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
x2 + 6x + 5
Factor each trinomial. Check your answer.
1 5x x
Holt Algebra 1
8-3 Factoring x2 + bx + c
3 3x x ProductSum
Factor each trinomial. Check your answer.
x2 + 6x + 9
23x
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
5 3x x
Factor each trinomial. Check your answer.
x2 – 8x + 15
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
3 2x x
Factor each trinomial. Check your answer.
x2 – 5x + 6
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
6 7x x
Factor each trinomial. Check your answer.
x2 + 13x + 42
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
8 5x x
Factor each trinomial. Check your answer.
x2 – 13x + 40
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
4 5x x
Factor
x2 + x – 20
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
6 3x x
Factor each trinomial.
x2 – 3x – 18
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
3 5x x
Factor each trinomial. Check your answer.
x2 + 2x – 15
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
4 2x x
Factor each trinomial. Check your answer.
x2 – 6x + 8
Holt Algebra 1
8-3 Factoring x2 + bx + c
ProductSum
10 2x x
X2 – 8x – 20
Factor each trinomial. Check your answer.
Holt Algebra 1
8-3 Factoring x2 + bx + c
A polynomial and the factored form of the polynomial are equivalent expressions. When you evaluate these two expressions for the same value of the variable, the results are the same.
Holt Algebra 1
8-3 Factoring x2 + bx + c
3 7y y
Factor y2 + 10y + 21. Show that the original polynomial and the factored form have the same value for y = 0, 1, 2, 3, and 4.
Holt Algebra 1
8-3 Factoring x2 + bx + c
Evaluate the original polynomial and the factored form for y = 0, 1, 2, 3, and 4.
(y + 7)(y + 3)
(0 + 7)(0 + 3) = 21
(1 + 7)(1 + 3) = 32
(2 + 7)(2 + 3) = 45
(3 + 7)(3 + 3) = 60
(4 + 7)(4 + 3) = 77
y
0
1
2
3
4
y2 + 10y + 21
02 + 10(0) + 21 = 21
y
0
1
2
3
4
12 + 10(1) + 21 = 32
22 + 10(2) + 21 = 45
32 + 10(3) + 21 = 60
42 + 10(4) + 21 = 77
The original polynomial and the factored form have the same value for the given values of n.
HW pp.544-547/17-49 odd,53,62-76,77-83 odd,86-94
